Differential Equations Using Generalized Derivatives on Fractals

In a previous paper [] we introduced the notion of a \(\mu \)-derivative and showed how to formulate differential equations in terms of this derivative. In this paper, we extend this approach to the definition of a weak derivative which provides a framework for solving variational problems with respect to fractal measures. We apply our method to a specific boundary value problem, namely a 1D eigenvalue problem over a fractal measure.